Scale Conversion Formula By: Rob Johnson (robj@speechsys.com)

Scales are ratios of measures in like units: 1/72 is 1 inch on the model = 72 inches on the full-sized original (or 1 centimeter, furlong, or parsec on model to 72 of same at full size).
The desired scale is then the existing scale times some unknown percentage or fraction, i.e. the conversion factor (either enlargement or reduction):
DesiredScale = ExistingScale * ConversionFactor
Therefore, to find the conversion factor, we regroup and divide to get the universal scale conversion formula:
ConversionFactor = DesiredScale / ExistingScale
Example: to convert 1/72 to 1/48
ConversionFactor = 1/48 / 1/72 = 72 / 48 = 1.5 = 150%
A 6-ft (72-inch) pilot figure is thus 1-in tall in 1/72 scale and 1.5-in tall in 1/48 scale.
Advantages of the formula: You can always figure out the intermediate ratios correctly when using photocpier enlargement. In the above example, most copiers would not do the full 150% in one pass. Most copiers max out at 121% or 141%. I have seen almost every other possible figure too. So having a chart of common scale conversions is not likely to be all that useful in many cases. Using the formula, you just figure out what the scale will be after the 121% enlagement:
IntermediateScale = ( ExistingScale * .121) + ExistingScale.
Then you use IntermediateScale as the ExistingScale in the formula.

## 2 comments:

am ot always awake enough, but gatherig the above formulay scale down from 20mm to 15 is 75% and up from 12mm is 144%. thats easy

Converting Between Scale Types

To theoretically convert ratio scales into height scales - and assuming here that height scales measure to "eye height" while ratio scales measure to "head height" - divide 1610 by the scale. For example, 1/285 figures are pretty much the same scale as

1610 / 285 = 5.65

6mm figures.

The reverse is also true: to get ratio scale, divide 1610 by the height scale. Thus, 25mm figures are equivalent to

1610 / 25 = 64.4

1/64 scale (which is in spitting distance of 1/72 scale, another common scale).

This means that 15mm toy soldiers are probably about 16.5mm tall overall, which makes them closer to 1/110 scale than 1/120. N-gauge figures (1/160) are about 11.25mm tall to the top of the head, which makes them about 10mm scale toy soldiers.

Where does the Magic Number 1610 Come From?

To get the magic number, all you need to come up with the "eye height" of the average man, measured in millimeters. The number we use is 1610 mm (about 5' 3").

Why does the magic number work? Because equivalent height and ratio scales, multiplied, should always result in the same constant (our magic number). In the simplest case, we take real life - 1:1 ratio scale, eye height of 1610 mm - and multiply 1 x 1610 = 1610. Therefore, 1610 is the constant.

So what is the magic number for a manufacturer who measures height scale to top of the head, rather than to eye level? Simply the height of the average man in millimeters - 1730 (5' 8").

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